预给极点的二元连分式插值

Bivariate Continued Fraction Interpolation with Prescribed Poles

文章建立了一种新的二元连分式插值,分析了其三项递推公式与特征定理,对其不可达点的修正处理方法进行了讨论,在已知被插值函数极点信息的情况下,获得了新的预给极点的二元连分式插值,该插值函数能够更好地区分极点的位置和保持原有的重数。数值算例证明了该理论的有效性和合理性。

A new bivariate continued fraction interpolation is set up in this paper.The three-term recurrence relation and characterization theorem are analyzed.At the same time,the correction method of its unattainable points is further discussed.Then,in the case of knowing the poles information related to the interpolated function,a new bivariate continued fraction interpolation with the prescribed poles is obtained,which can better distinguish the position of the poles and maintain the original multiplicity.Finally,numerical examples are given to verify the effectiveness and consistency of theory in the paper.